Many types of medical instruments, such as an infrared (IR) thermometer, contain a probe for insertion into a body cavity so that various body related measurement can be taken. In order to prevent cross contamination between patients or health care workers and patients, the probe is generally enclosed within a protective cover which can be disposed of in a sanitary manner after it has been used. Typically the covers are manufacted of plastic using different types of molding techniques many of which produce products that have surface imperfections or which can not be held to tight tolerances. Most protective covers are packaged and shipped with the covers being stacked one inside the other. Unstacking irregular formed covers and placing them upon the tip of an instrument can be extremely difficult. Defective covers tend to bind in the stack and as a consequence can be damaged and dropped during removal from the stack. Displacement or a misshapened cover from the instrument tip during an examination can also be unnerving to both the attending health care individuals and the patient. Lastly, an irregular formed covers can hang up on the instrument during removal thus requiring unwanted manual handling of a potentially contaminated product.